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Matlab+统计分析.pdf

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1、MatlabBXCGC6C9C7BGDAC6AUA4APANCKA1CBDJB9BT MatlabD0BCBABK 11.1 C5AVA8CB . 11.1.1 B2A0C5AVA0BAB9 . 11.1.2 C5AVA0A8CB 21.1.3 BYCCA0A8CB 51.1.4 CIANA8CB . 61.1.5 ANAHA8CB . 61.1.6 C5AVA8CBCVBY. 71.1.7 ADAYCVBY . 91.2 CQBGDCCB 101.2.1 for BWDIDCCB . 101.2.2 while BWDIDCCB 111.2.3 if CY break DCCB . 121.

2、3 ABB5 131.3.1 M ABB5 131.3.2 CVBYABB5 . 131.3.3 ABB5A0BQCMA2CYBQCM . 141.4 A7D6 151.4.1 ATA3A7D6 . 151.4.2 A6A3A7D6 . 171.5 CW MATLAB BNDIB9B1CE 191.5.1 DIB9B1CEA6CCA8A0BNAKBN 201.5.2 DIB9B1CE (CC) A0BYB8BN . 211.6 CWDIB9B1CEB7DCBMD8AQCKB9BH . 251.6.1 DBBMD8AGC5B9BH . 2512 BHA0AG1.6.2 AQAID8CRA0C1A

3、XC0CIB9BH 271.7 D0CKC2A0CYCLCGBOCQA0A0DFBXADCQ . 291.7.1 ADCQA0CPCM 291.7.2 B9BHAXAK . 301.7.3 B7DCB9BH . 301.7.4 CYBNCSCE . 31DJA5BT D8BEAFB3ADATA9A7 352.1 BPAJAMCLBJ 352.1.1 BPAJ 352.1.2 CDB7A0 . 362.1.3 C4CWA0B9BI 392.2 BRBYCEAP . 422.2.1 A5CEAP 432.2.2 CEAPA0A0CXDIBKC0AF . 502.2.3 D0AZCEAP . 542

4、.3 AXAKB0C7 . 612.3.1 AZCKC8CRCEB8A0AXAKB0C7 622.3.2 AZCKC8CRB1C1A0AXAKB0C7 662.4 A4COB9AK . 682.4.1 CEDGAWBKA4CO. 692.4.2 AQDGAWBKA4COB9AK 712.4.3 BQBJA4CO . 792.5 B1C1B9AK . 822.5.1 DBCQC8B1C1B9AK . 832.5.2 BZCQC8B1C1B9AK . 942.6 C1BBB9AK . 1022.6.1 CAD6C1BB . 1022.6.2 Fisher C1BB 109BHA0AG 3DJD2B

5、T BECHD8B5 1153.1 DIB9B1CEB3C7 1153.1.1 B3C7BHA0 . 1153.1.2 B3C7C9CY . 1153.1.3 ADAYB3C7 . 1153.1.4 B9CCBYDH . 1173.2 BYD7D5APDBCDB9BSB3C7 1183.2.1 B3C7BHA0 . 1183.2.2 B3C7C9CY . 1183.2.3 ADAYB3C7 . 1183.2.4 B9CCBYDH . 1224 BHA0AGA0BABU Matlab D1BDBBBLMatlabA0CTCNBCC5AVB3C7BHA6 Matrix LaboratoryA8AA

6、BCAVCQ MathWorkC9C5D6 1982 BVD9CMA0CECNBVBKBPA0BYB8APCBCYCLBIDFA3B5AACIAIBYB8B9AKA2C5AVAPCBA2BFCXCRD7CYD6BIASB9D6CECRAACBCBCEC0B1B6A0A2BOB3D3CWA0CWDCDIBZA3DHBHCNA2BAAACICIAUAHCBA2CQASAFCECXBLA0CKAOCTCWA3B5B3CEA31.1 BPBWBQA4Matlab A3B5CEADAYA0DCCBBCC5AVA8CBAACICLCKB5C4B1B6A3DCCBB2A0A2C5AVA0C1BMA8CBAA

7、A1B2A0A0AVAVDBBYCDAAC5AVA0AVAVA2BYCDA2CDAVA2CNAVA6CYBUA8CYCDB1A1A8CBA31.1.1 AYC6BOBVDHCSDB1. BJB2A0x=-102 % BKAZCWCPBYB8BYC7B9CGAACACLCKCWCXB9CGx= % ASB9BQA2BMCR-102AB Matlab A3B5BKAA % D8A0DCCBBCC3B6DCCBA32. A3B2A0 y = 3 8 2 %BAB9BXBFy=3823. C5AVA=123;456;780 %;BAB9A0BJA=12345678012 A8B2BY Matlab B

8、QCFCDCQ4. BXBF B = AB=1472583601.1.2 BOBVDHBPA3ABAQD8BQAH Matlab A3B5A0C1BMADAYA8CBA3AQB7A8CBASCW+ AV B2 CD / D4CN CHCN CDB1ABBYB8A8CBBKCHCNDBD4CNBCCEC8A0AAA1 1/4 DB 41 AACGBMCRCEA2 0.25 AADDAOC5AVA8CBAFBMCRD6BHAXD3A31. AVB2AVC=A+B % DJC5AVA0A3BYB2BMAXD3C=26106101410 14 0DDC5AV A CLCKDBCEC0BYC6AXAVA

9、AA1 A + 2ans =345678910 2AXDFD6AUC0DGC8 +2, AOD6B2A0CAD2D3C8A0BMCRA3A1 x + 2ans =1242. CDAVC5AVAXCDAAA1D=A*B % DJC5AVB2BMARCAC5AVCDAVCNAF1.1 C5AVA8CB 3D=14 32 2332 77 6823 68 113CYBYCDA8CBAAAKCWA0DBC5AVAXCDAAA1 2 * Aans =2468101214 16 0ABDBDJD2A5CDA8CB C = A. * BC=18218254821 48 0BAB9 cij= aij bij,

10、CGBK C =(cij), A =(aij), B =(bij).3. C5AVCYBU inv(A) %invCVBYBCCYBUA8CBCVBYans =-1.7778 0.8889 -0.11111.5556 -0.7778 0.2222-0.1111 0.2222 -0.1111BCC5AV A A0BUC5AV A1. CQCX I = inv(A)*AI=1.0000 0.0000 00.0000 1.0000 00.0000 0 1.0000BCDBA8C5AVA34 A8B2BY Matlab BQCFCDCQ4. C5AVCNAV b = 1 1 1; % BQA2B2A0

11、 bx=Ab % CHCNA8CBx=-1.00001.00000.0000BAB9B1CECC Ax = b A0BNAAAK x = A1b. AOD6C7ACB1CECCC5AVCNAVBAB9CEB5ATCDBNAAA1 X = 1 1 1 1 1 1 1 1 1 1; 1 0 2 0 3 1 0 1 2 0; y = 16 9 17 12 22 13 8 15 19 11; beta = X ybeta =10.20004.0000AK =parenleftbigXTXparenrightbig1XTy.5. CDB1 D = A2D=30 36 1566 81 4239 54 69

12、AK D = A2. D3C8CAD2A5A8CBAAA1 G = A. 2G=14916 25 3649 64 0AK gij= a2ij, CGBK G =(gij), A =(aij). G = A. B1.1 CYC2BTCS 5G=1 16 218716 3125 1679616343 262144 1AK gij= abijij, CGBK G =(gij), A =(aij), B =(bij).1.1.3 DHC9DHBPA3AB Matlab BKAABYCCA2B2A0CYC5AVAAD2B0CMCNBCAXD3A0A31. BYCCAVB2AV x = 1 2 3; %;

13、BAB9BHASB9BQA2B8 y = 4 5 6; x + yans =5792. BYCCCDAV z = x. * yz=41018AK zi= xi yi, CGBK z =(z1,z2,z3), x =(x1,x2,x3), y =(y1,y2,y3).3. BYCCCNAV z = x. yz=4.0000 2.5000 2.0000CHCNBAB9 zi= yi/xi, CGBK z =(z1,z2,z3), x =(x1,x2,x3), y =(y1,y2,y3). z = x. / yz=0.2500 0.4000 0.5000D4CNBAB9 zi= xi/yi,CGBK

14、z =(z1,z2,z3), x =(x1,x2,x3), y =(y1,y2,y3). BVCMADCHCND4CNCMCNBHCEC8A34. BYCCCDB16 A4CEAK Matlab A3B5B1BQ z = x. yz=1 32 729BAB9 zi= xyii, CGBK z =(z1,z2,z3), x =(x1,x2,x3), y =(y1,y2,y3). ABDBDJD2 z = x. 2z=149BAB9 zi= x2i, CGBK z =(z1,z2,z3), x =(x1,x2,x3). z = 2. yz=16 32 64BAB9 zi=2yi, CGBK z =

15、(z1,z2,z3), y =(y1,y2,y3).1.1.4 ALAVBPA3AOD6C5AVA2B2A0CYBYCCD2A1APCIANA8CB D6D6=D6D6A1D6 = A1D6 =BHA1D6A1CRCIANCBDCAFA2AXA4B8A2 1 AFBCAFAXA4B8A2 0. A1 a = -1 2 4; 5 4 -8;c=a0c=0111101.1.5 CFB2BPA3ABCYB5DCCBBKD2A1APANAHA8CB4 5 6; 7 8 0; det(A)ans =272. A6BEB9BNA6 lu()A8A6BEB9BNCAC8A2 LU B9BNAAB8C5AV

16、A B9BNCBCEC0DBA8APA6BEAVCYCEC0AFA6BEAVA0CDAFAAAK A = LU. AB Matlab BKCZCVBY lu DCCBCXC6CJAACIAOC5AV A BOCWBSD2BRDGA0 LU B9BNA3A1 L, U = lu(A) % A3BRDG LU B9BNA3L=0.1429 1.0000 00.5714 0.5000 1.00001.0000 0 0U=7.0000 8.0000 00 0.8571 3.00000 0 4.50003. AZBCB9BNA6 qr()A8AZBCB9BNCAC8A2 QRB9BNAAB8C5AV A

17、B9BNCBCEC0AZBCAV QCYCEAFA6BE RA0CDAFAAAK A = QR.qrCVBYDCCB QR B9BNA0C6CJA3 A = 1 2 3;4 5 6;7 8 9;10 11 12; Q, R = qr(A) %QRB9BNQ=-0.0776 -0.8331 0.5444 0.0605-0.3105 -0.4512 -0.7709 0.3251-0.5433 -0.0694 -0.0913 -0.8317-0.7762 0.3124 0.3178 0.4461R=8 A8B2BY Matlab BQCFCDCQ-12.8841 -14.5916 -16.29920

18、 -1.0413 -2.08260 0 0.00000004. CHCPB8B9BNA6 svd() A8B8C5AV AB9BNCBAZBCAV U A2AOBEAV S CYAZBCAV V A0CDAFAAAK A = USVT. U, S, V = svd(A) % CJCHCPB8B9BNA3U=0.1409 0.8247 0.5477 0.00780.3439 0.4263 -0.7361 0.39770.5470 0.0278 -0.1709 -0.81900.7501 -0.3706 0.3593 0.4134S=25.4624 0 00 1.2907 00 0 0.00000

19、00V=0.5045 -0.7608 0.40820.5745 -0.0571 -0.81650.6445 0.6465 0.40825. COAWB8B9BNA6 eig() A8CYC5AV A A0COAWB8CYAXCTA0COAWB2A0A3 A = 1 2 3; 4 5 6; 7 8 9; Q, D = eig(A)Q=0.2320 0.7858 0.40820.5253 0.0868 -0.81650.8187 -0.6123 0.4082D=16.1168 0 01.1 C5AVA8CB 90 -1.1168 00 0 0.0000CGBK D A0AOBEDGC8 diiBC

20、C5AV A A0A4i C0COAWB8AA Q A0A4i A3BCAOCTA4 i C0COAWB8A0COAWB2A0A31.1.7 AZCPAPDH1. ADAYCLA1CVBYsin AZAR cos D7AR tan AZCQ abs CYCDAOB8sqrt CGB1 exp B9BY log AOBYAB Matlab A0CVBYA8CBBKAACVBYA0B7A0CLCKBCBYA2B2A0A6BYCCA8CYC5AVA3A1CRC5B7A0BCBYA2B2A0A6BYCCA8CYC5AVB0AAAOCTA0CQB7A0CABCBYA2B2A0A6BYCCA8CYC5AV

21、A32. DBC5AVD2CIA0C4CWCVBY(1) norm CVBYA3CYC5AVABB2A0A0 2B9A6 2AYBYA8A3A1A=123;456;789; norm(A)ans =16.8481(2) cond CVBYA3CYC5AVA0CYB5BYA3A1 cond(A)ans =3.7740e+016(3) rank CVBYA3CYC5AVA0BHA3A1 rank(A)ans =2(4) zeors CVBYA3AQCBA8C5AVABA8B2A0A3A1AQCBCEC0 1 BJ 3 A3A0A8C5AVA6B2A0A8 a = zeros(1,3)a=00010

22、 A8B2BY Matlab BQCFCDCQ(5) onesCVBYA3AQCBDGC8A2 1A0C5AVABB2A0A3A1AQCBCEC0 1BJ3A3DGC8A2 1A0C5AVA6B2A0A8 b = ones(1,3)b=111(6) eye CVBYA3AQCBDBA8C5AVABDBA8B2A0A3A1AQCB 3 3 BJDBA8C5AV I = eye(3)I=100010001(7) size CVBYA3CYC5AVD6B5A6A3BYA8A3A1size(A)ans =33BAB9C5AV A BC 3 3 BJA0A3(8) length CVBYA3CYB2A0

23、A0C5AIA6A3BYA8A3A1 length(b)ans =3BAB9B2A0 b BC 3 A3A0A31.2 BXC1C9BLBT1.2.1 for B3AUBKBSfor BWDIDCCBBYB8A2for BWDIB7A0 % B7A0CZBDB8CGB7AADHBDB8BMBXAAA1 for i=1: nDCCB % BWDICRBKA0B7BJDCCBend % BWDIDHCXCZ for CGB7AA end BMBXAACLCKCOCNA3A11.2 CQBGDCCB 11for i = 1: 5for j = 1: 5a(i,j) = 1/(i+j-1);enden

24、da=1.0000 0.5000 0.3333 0.2500 0.20000.5000 0.3333 0.2500 0.2000 0.16670.3333 0.2500 0.2000 0.1667 0.14290.2500 0.2000 0.1667 0.1429 0.12500.2000 0.1667 0.1429 0.1250 0.11111.2.2 while B3AUBKBSwhile BWDIDCCBBYB8A2while CYB5 % CYB5CBDCB0B7BJAACYB5BHCBDCBLBADCCBendB5BCCEC0APCB 1000CKBOA0 Fibonacci BYf

25、 = 1 1;i=1;while f(i) + f(i+1) 1if rem(n,2) = 0n = n/2;elsen=3*n+1;endendendABCEBQBKAA remBCD3D7CVBYA31.3 DICF 131.3 ANBD1.3.1 M AMBCABMatlabBKCLCKB8CECYCECYA0B8ACB5CBCEC0 MABB5AACECID3B7BJA3DBA1B8APCB 1000 CKBOA0 Fibonacci BYA0B8ACf = 1 1;i=1;while f(i) + f(i+1) x=1 2 3 4; 3 4 5 6; mean,std=stat(x)

26、mean =2.5000 4.5000std =1.1180 1.1180AB M ABB5BKAAC3B6DCCBD3BNC9AACICLCKCPC8CEBQA0C3B6AAAB Matlab BKAACLCWhelp B8ACCLCKASB9 M ABB5BKA8D6ABB5BKCECLCEBJA6ABAMBJA8A0C3B6DCCBA31.3.3 AMBCDHDEDDCZAQDEDDMatlab A0BQA2BQCMABB5DB C DCC3A0BQA2BQCMABB5ADAYAXD3A3DBA1AD1. D5CGABB5D5CGABB5A0B8ACBYB8A2fid = fopen(

27、ABB5B7, A7BPD4BH)A7BPD4BHD2r BBAHBH w BBBCBHa CUAVBH r+ AHBCBH2. CIB1ABB5CIB1ABB5A0B8ACBYB8A2fclose(fid)3. BCABB5BCABB5A0B8ACBYB8A2fprintf(fid, BYB8)BYB8D4BHD2%d AYBYBYB8 %f BGA5BYB8%e B9BYBYB8 %g BGA5BYB8CYB9BYBYB8%s C6BEBYB8 n A0BJDBA1AAx = 0:.1:1; y = x; exp(x);1.4 BSDB 15fid = fopen(exp.txt,w);f

28、printf(fid,%6.2f %12.8fn,y);fclose(fid)BCCEC0BG exp.txt A0ABAYABB5AAA4BNABB5BHD1ABAAAFAQCBCEC0BDABB5AFA4BNABB5CID1ABAAAFBDABB5BIBQDHABB5A34. AHABB5AHABB5A0B8ACBYB8A2fscanf(fid, BYB8)A1S = fscanf(fid,%s) % AHCEC0C6BECTA = fscanf(fid,%5d) % AH 5 A8BYA0AYBY1.4 AYAI1.4.1 A5ALAXAH1. DDCVBYD1AWCYA7A5D6DDC

29、VBYD1AWCYA7A5D6A0B8ACBYB8A2plot(x,y,s)CGBK x BCD4CKB9AAy BCC9CKB9AAsBCCLBSBRBYA6ARD6A2B3AWA8AACGCMCNB3APBABRBY C4A9 BRBY AQCX BRBY D1AWy A2A9 . A5 - B3AWm CAA9 o DJD4 : BNAWA6CZA5CBCBA8c CSA9 x BY -. BNAWA6CZAWA5CBCBA8r D6A9 + AVCX - BNAWA6CZAWALCBCBA8g AKA9 * BGCXb D0A9 s B1CSw AKA9 d CDAZk D2A9 v

30、APA6BEDBA1AAAB 0, 5 AFDDCM y = ex4sin x2A0D1AWA316 A4CEAK Matlab A3B5B1BQx = 0: 0.05: 5;y = exp(-x/4). * sin(x. 2);plot(x,y)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.60.40.200.20.40.60.82. B5B1D6CWbarCVBYCLCKDDCMD1AWD2B5B1D6A3A1DD y = ex2AB 3, 3AFA0B5B1D6A3x = -3:0.2:3;bar(x,exp(-x.*x);4 3 2 1 0 1 2 3 400.10

31、.20.30.40.50.60.70.80.913. AGCKB9D6BICWpolar CVBYCLCKDDCMD1AWA0CKB9D6BIA3DBA1DDCM = |sin 2tcos 2t|ABCEC0BOCFAFA0AGCKB9D6BIA3t = 0: 0.01: 2*pi;polar(t,abs(sin(2*t).*cos(2*t);1.4 A7D6 170.1250.250.3750.5302106024090270120300150330180 01.4.2 D2ALAXAH1. DEBYD1B3CWmeshCVBYCLCKDDCMA6A3DEBYD1B3A3DBA1DDCM z

32、 =sinx sin yABD0DD, , AFA0DEBYD1B3A3x = -pi:0.3:pi; y = -pi:0.3:pi;X,Y = meshgrid(x,y);Z = sin(X).*sin(Y);mesh(X,Y,Z)432101234202410.500.512. BAB3D1B318 A4CEAK Matlab A3B5B1BQCWsurfCVBYCLCKDDCMA6A3BAB3D1B3A3DBA1DDCM z =sinx sin yABD0DD, , AFA0BAB3D1B3A3surf(X,Y,Z)432101234202410.500.513. A1BVAWA6A1B

33、8AWA8CW contour CVBYCLCKDDCMD1B3A0A1BVAWA3DBA1DDCM z =sinx sin y ABD0DD, , AFA0A1BVAWA3contour(X,Y,Z,16) AACGBK 16 A2A1BVAWA0CYBYA33 2 1 0 1 23210121.5 CW MATLAB BNDIB9B1CE 193. A6A3D1AWCW plot3 CVBYCLCKDDCMBRBYB1CEx = x(t)y = y(t)z = z(t),t ,C2CMA0A6A3D1AWA3DBA1DDCMx =costy =sintz =0.1t,t 0, 6A0A6A

34、3D1AWA3t = 0:0.03:6*pi; x = cos(t); y = sin(t); z = 0.1*t;plot3(x,y,z)10.500.5110.500.5100.511.521.5 BF MATLABBJAKAADAMatlabCPC8A1AQD330AQC0B3B2BHD3AADDASCXAHA0C6C9AY (ToolBox)B1CGAAASCWADD2BFC6CEA2BFCXCRD7A2D6BICRD7A2B5AWBKCQBGA2APBYDEAPA2CXDFCRD7A220 A8B2BY Matlab BQCFCDCQCWD5APB9AKA1D6A0ATD8C6CEA

35、OBUBTCKA0BODJA3B6DJ MatlabABBPAQBTCKAADDBKCBA2APCBBHBTB9AKDBAKAPA2CBAVC1C2CYCTCWCGAUA0ADAYC6C9CYBMBSCACJA3AYBLB1DBBQAHCEAPCWCIBNDIB9B1CEA0C7BPA31.5.1 AJADA9D9A6C9A8DHBIATBICYDIB9B1CEA6CCA8A0BNAKBNCWCVBY dsolve.CYBNDIB9B1CEB0AABMC9B8DIB9B1CEASCTAB dsolveA0BAD3B8BKAAABBAD3DIB9B1CEB0AACWC6BF DBAB9CYDIB

36、9AAD2, D3A1BAB9CYBVBJDIB9AADDCZ D D8CGC4C6BFA2CQB7A0AAC5B7A0CLCKB9ACABCZ symvar CNAFBSACA2D6ARAADBA1DIB9B1CEd2ydx2+3dydx=2CLBAD3A2 D2y+3*Dy=2. AXD2CSA4BSDBC4C3B6BNAVA3C11.1BEdudt=1+u tA4D7CPA3BNADB8ACdsolve(Du=1+u-t, t), BMCRA2ans = t+exp(t)*C1AK u(t)=t + Cet.C11.2BEA7A4DEATAOD3A4D0CPA3braceleftBigg

37、d2ydx2+4dydx+12y =0y(0) = 0,yprime(0) = 5BNADB8ACy=dsolve(D2y+4*Dy+12*y=0, y(0)=0, Dy(0)=5, x), BMCRA2y = 5/4*2(1/2)*exp(-2*x)*sin(2*2(1/2)*x)AKy(x)=524sin(22 x) e2x.C11.31.5 CW MATLAB BNDIB9B1CE 21BEA7A4DEATAOD3CQA4D0CPA3dxdt=2x 3y +3zdydt=4x 5y +3zdzdt=4x 4y +2zBNADACx,y,z=dsolve(Dx=2*x-3*y+3*z,Dy

38、=4*x-5*y+3*z,Dz=4*x-4*y+2*z,t)BMCRA2x = exp(2*t)*C1+C2*exp(-t)-C2*exp(2*t)+exp(2*t)*C3-C3*exp(-t)y =-C1*exp(-2*t)+exp(2*t)*C1+C2*exp(-2*t)+C2*exp(-t)-C2*exp(2*t)+exp(2*t)*C3-C3*exp(-t)z =-C1*exp(-2*t)+exp(2*t)*C1-C2*exp(2*t)+C2*exp(-2*t)+exp(2*t)*C3AKx(t)=C1e2t+ C2(et e2t)+C3(e2tet),y(t)=C1(e2t e2t)

39、+C2(e2t+ et e2t)+C3(e2t et),z(t)=C1(e2te2t)+C2(e2te2t)+C3e2t.1.5.2 AJADA9D9 (C9) DHDHC0BIBDB7BKA9A0DIB9B1CEA6CCA8AAD2B0D3BLCYCMCIA0BNAKBNAACXB0C9AKAVCYCGBYB8BNA3B1AVB3CEB6BCCW MATLAB BKCYDIB9B1CEA6CCA8BYB8BNA3AXCIA0BYB8BNCVBYD2AHC0ode45, ode23, ode113, ode15s, ode23sCEBQA2t,x=solve(f, ts, x0, option

40、s)AFBVB8ACBJBKAAsolve BCCKAFAHC0CVBYB3CEAABHD3A0CVBYD8BABHD3A0BOBKCBAVACC4CWCVBYA2 ode45.fBCCZD9BNB1CEBCCBA0 m-ABB5B7AFts=t0, tf, t0, tfA2C5B7A0A0CLB8CYBLB8AF x0A2CVBYA0CLB8AF options CWD6AKACAJC1AV (CLCKD6ARAACXB0AXAOAJC1A2 103, CDAOAJC1A2 106), CEBQBIB8A222 A4CEAK Matlab A3B5B1BQoptions=odeset(rel

41、tol, rt, abstol, at)AQD8 rt, atB9BBA2AKACA0AXAOAJC1CYCDAOAJC1ACABBN nC0A5B2CVBYA0B1CECCB0AAx0CYxCEA2 n A3B2A0AAm-ABB5BKA0D9BNB1CECCCTCK xA0B9A0BIB8BCCMACC11.4Lorenz AOANA4CKCYAOD3CQD6CKCBDFADxprime1(t)=x1(t)+x2(t)x3(t)xprime2(t)=x2(t)+x3(t)xprime3(t)=x1(t)x2(t)+x2(t) x3(t)BRA8 =10, =28, =83,BCD7C8DF

42、 x1(0) = x2(0) = 0, x3(0) = , DFB2B3AGCYCKAACABZ =1010, BEDAAOD3A4CKC8CPA3BNADB7DCB4BVDIB9B1CECCA0 m-ABB5 lorenzeq.m.function xdot=lorenzeq(t,x)xdot=-8/3*x(1)+x(2)*x(3);-10*x(2)+10*x(3);-x(1)*x(2)+28*x(2)-x(3);AQC8C3CLCKDACWAPB3DCCBt_final=100; x0=0;0;1e-10;t,x=ode45(lorenzeq,0,t_final,x0);plot(t,x)

43、,figure; plot3(x(:,1),x(:,2),x(:,3);axis(10 40 -20 20 -20 20);BNCMBNDIB9B1CECCA0BNAAA7BGCMB0AZD1AWDBAXCPAZD1AWAAA1D6 1.5.1 CY 1.5.2 CGB9A3C11.5BECPALCIC1A0B9A4CVAAA4 Verderpol DEATAOD3braceleftBiggd2ydt2(1 y2)dydt+ y =0,y(0) = 1,yprime(0) = 0.1.5 CW MATLAB BNDIB9B1CE 230 10 20 30 40 50 60 70 80 90 1

44、0030201001020304050x (t) x (t) x (t) 1 2 3 D61.5.1: BZCKB7A0A0B0AZB0CTD6D1AWAC10152025303540201001020201510505101520D61.5.2: AXCPAZA6A3D6D1AWACBNADBMAQB8BVBJDIB9B1CEA1AYA3B7CBCEBJDIB9B1CECCAAD9D8AABNDJDHA0DIB9B1CECCAACZASDJDHBYB8BNA324 A8B2BY Matlab BQCFCDCQAC x1= y,x2=dydt, AFDIB9B1CEBXDFA2DIB9B1CE

45、CCdx1dt= x2,dx2dt= (1 x21)x2x1,x1(0) = 1,x2(0) = 0.B5BCCVBYABB5 verderpol.mfunction xprime = verderpol(t,x)global muxprime = x(2); mu*(1-x(1)2)*x(2)-x(1);ABB8ACCUCRBKB7BJglobal mumu = 7; Y0=1 0;t,x=ode45(verderpol,0 40,Y0);x1=x(:,1); x2=x(:,2);plot(t, x1, k-, t, x2, k-)DJ xDB tA6B3AWA8AA dx/dt DB tA

46、6BNAWA8A0CIAND6AAA1B3D6 1.5.3 CGB9A30 5 10 15 20 25 30 35 4015105051015D61.5.3: x(t)DBdx(t)dtA0D1AWACABCEBMCW Matlab CYBNBNDIB9B1CEA0BIB8A3BMAQB7DC.mABB5 vdp.mfunction dx=vdp(t, x)1.6 CWDIB9B1CEB7DCBMD8AQCKB9BH 250 5 10 15 20 25 30 35 402.521.510.500.511.522.5D61.5.4: t x(t)A0D6BIACglobal mudx=zeros

47、(2, 1);dx(1)=x(2);dx(2)=mu*(1-x(1)2)*x(2)-x(1);AAD2 t0=0, tf=40, BQA2B8ACglobal mumu=7;t, x=ode15s(vdp, 0 40, 1 0);plot(t, x(:,1),-);DJ xDB tA0CIAND6AAA1D61.5.4 CGB9A3AQD8BTBQAHA4BSC4CWA0AMC0B8ACAJCGCTCWAAD2CIAOBLCWAHAPBRCIAXCIBRCIBRAC1.6 BFAKAADABFC3C3CYD7A8CIB1BDB7AQAIBMD8A6ASCWDCCR), CZD6C8A0C8D6AAC2B0BOB7A0A0AXAODIB5AACEAMCLBVC7A2B0AZA0DFBRCLDICVBYAACZASCLDACWDIB9 (ABC1B9) B1CECYB7DCB9BHA31.6.1 DFC2CXBSD8CHB01. Malthus B9BH

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